Math Problem Statement

Graph the line y = -x - 5

Solution

The equation provided in the image is:

y=x5y = -x - 5

This is a linear equation in slope-intercept form, y=mx+by = mx + b, where:

  • m=1m = -1 is the slope of the line.
  • b=5b = -5 is the y-intercept, the point where the line crosses the y-axis.

To graph this line:

  1. Start at the y-intercept: The line crosses the y-axis at (0,5)(0, -5).
  2. Use the slope: The slope is 1-1, which means for every unit you move to the right along the x-axis, move down by 1 unit on the y-axis. This gives the direction of the line.
  3. Plot another point: From (0,5)(0, -5), move right by 1 and down by 1 to find another point (1,6)(1, -6).
  4. Draw the line: Once you have two points, you can draw a straight line through them, extending in both directions.

Would you like a detailed graph or any further explanations?

Related questions:

  1. What is the slope of the line, and how does it affect the direction of the line?
  2. How do you determine the y-intercept from a linear equation?
  3. Can we express this equation in another form, such as point-slope form?
  4. What happens if we change the slope to a positive value?
  5. How would the graph change if the constant 5-5 was replaced with a different number?

Tip: To graph any linear equation quickly, always identify the slope and y-intercept first. These give you the key points to plot the line.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Linear Equations
Graphing

Formulas

Slope-intercept form y = mx + b

Theorems

Slope of a Line
Y-intercept

Suitable Grade Level

Grades 7-9